Internal problem ID [7838]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 258.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y x^{2} y^{\prime }+y^{2}-2 x^{3}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 33
dsolve(2*x^2*y(x)*diff(y(x),x)+y(x)^2-2*x^3-x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+x^{2}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{\frac {1}{x}} c_{1}+x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.075 (sec). Leaf size: 43
DSolve[2*x^2*y[x]*y'[x]+y[x]^2-2*x^3-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+c_1 e^{\frac {1}{x}}} \\ y(x)\to \sqrt {x^2+c_1 e^{\frac {1}{x}}} \\ \end{align*}